Spatial matching (‒s)
When states are to be matched, a wavelet decomposition of the gridded field can be used to give a better match than using the areal averages.
A wavelet level of 1 means that the domain resolution is decreased by a factor of 2 in each direction (that is, a grid 20x20 is decreased into one 10x10). A level of 2 gives a reduction of 4 in each direction.
wxgen sim -db db.nc -n 21 -t 365 -wl 3 -o sum.ncWavelets reduce the jumps at the local scale. Even a wavelet level of 4 (meaning that the domain is decomposed into a 2x3 grid) significantly reduces the jumps.
wxgen sim -db db.nc -n 21 -t 365 -w 1 -v 0 -o no_wl.nc
wxgen sim -db db.nc -n 21 -t 365 -w 1 -v 0 -wl 3 -o wl3.nc
wxgen sim -db db.nc -n 21 -t 365 -w 1 -v 0 -wl 4 -o wl4.nc
wxgen verif no_wl.nc wl4.nc wl3.nc -m jump -tm 9
Note that the jump statistics for the aggregated scale are not changed, since the non-wavelet approach does this well already.
Wavelets appear to reduce the variance of aggregated quantities:
